On the Problem of Reconstructing a Mixture of RNA Structures

A growing number of RNA sequences are now known to exist in some distribution with two or more different stable structures. Recent algorithms attempt to reconstruct such mixtures using the list of nucleotides in a sequence in conjunction with auxiliary experimental footprinting data. In this paper, we demonstrate some challenges which remain in addressing this problem; in particular we consider the difficulty of reconstructing a mixture of two RNA structures across a spectrum of different relative abundances. Although progress has been made in identifying the stable structures present, it remains nontrivial to predict the relative abundance of each within the experimentally sampled mixture. Because the ratio of structures present can change depending on experimental conditions, it is the footprinting data-and not the sequence-which must encode information on changes in the relative abundance. Here, we use simulated experimental data to demonstrate that there exist RNA sequences and relative abundance combinations which cannot be recovered by current methods. We then prove that this is not a single exception, but rather part of the rule. In particular, we show, using a Nussinov-Jacobson model, that recovering the relative abundances is difficult for a large proportion of RNA structure pairs. Lastly, we use information theory to establish a framework for quantifying how useful auxiliary data is in predicting the relative abundance of a structure. Together, these results demonstrate that aspects of the problem of reconstructing a mixture of RNA structures from experimental data remain open.